It is known that digital transmission system performance can be improved by the use of codes admitting error correction by decoders at the receiving side. This allows either bit error rate reduction for a given power of the transmitted signal, or transmission with reduced power for a given bit error rate. The latter possibility is of great interest for applications as the one above, and the so-called "coding gain" (i.e. the decrease of ratio Eb/No between the energy transmitted per bit and the power of Gaussian white noise) expresses the performance improvement achieved.
It has already been described in the literature that error correcting codes of the FEC type (FEC=Forward Error Correction, i.e. correction without block repetition) afford a certain coding gain in case of mobile radio systems, and that by supplying the decoder with some information on the channel state, performance can also be improved in terms of bit error rate. More particularly the papers entitled "Performance and burst error characteristics of PAM/FM modulations in mobile radio channels" presented by G. D'Aria, G. Taricco and V. Zingarelli at IEEE Global Telecommunications Conference, Houston (USA), 1-4 Dec. 1986, paper 31.4, pages 1110-1114, and "Burst error characteristics of narrowband digital systems in land mobile radio" presented by the same authors at the 36th IEEE Vehicular Technology Conference, Dallas (USA), 20-22 May 1986, pages 443-451, suggest that all errors (symbol substitutions) should be considered as erasures, i.e. the decoder should receive no information on the symbol actually present in a given location.
This suggestion is based on the fact that considering a location within a a codeword as an erasure can improve decoder correction capability, if such a location actually corresponds to an error. In fact an error correcting code with Hamming distance D can correct errors and erasures such that 2E+C.ltoreq.D-1, where E is the number of errors and C the number of erasures. Hence, if C=O, (D-1)/2 errors at most can be corrected, whereas if C=2 and the erasures correspond to erroneous symbols, (D-3)/2+2=(D+1)/2 errors at most can be corrected, with an actual improvement in the correction capability. This capability is, by contrast, reduced if an erasure corresponds to a correct symbol, since the decoder can correct only (D-2)/2=D/2-1 errors. Generally speaking, if the doctor has been signalled C=C'+C" erasures, C' corresponding to erroneous symbols and C" corresponding to correct symbols, the decoder can correct up to (D-1-C'-C")/2 +C'=(D-1+C'-C")/2 errors, with improved performance if C'&gt;C"+1 (with odd D). In the ideal case in which all errors can be detected as erasures and there are no erasures in correspondence with correct symbols (E=0, C"=0), it is clear that correction capability will be doubled.
The cited papers do not give any indication on how detection of at least some errors as erasures can be obtained practically.